Shot noise and transport in small quantum cavities with large openings

Nazmitdinov, R. G.; Sim, Hyun Sub; Schomerus, Henning; Rotter, I.

doi:10.1103/physrevb.66.241302

Cited by 31 publications

(51 citation statements)

References 36 publications

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“…Various RMT related aspects of the shot noise are under active study now, both theoretically 8,9,10,11,12,13,14 and experimentally 15,16 (see also the references in these papers). However, exact results for the average shot-noise power P were reported in the literature only in the limiting cases of N 1,2 ≫ 1 2,17 (which is the purely classical one) 8,18 or…”

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Shot noise in chaotic cavities with an arbitrary number of open channels

Savin

Sommers

2006

Phys. Rev. B

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Using the random matrix approach, we calculate analytically the average shot-noise power in a chaotic cavity at an arbitrary number of propagating modes (channels) in each of the two attached leads. A simple relationship between this quantity, the average conductance and the conductance variance is found. The dependence of the Fano factor on the channel number is considered in detail. 73.50.Td, 05.45.Mt, 73.63.Kv The time dependent fluctuations in electrical currents caused by random transport of the electron charge e, which (unlike thermal fluctuations) persist down to zero temperature, are known as shot noise. In mesoscopic systems, an adequate description of this phenomenon is achieved in the scattering theory framework.1,2 In particular, for the two-terminal setup (with a small voltage difference V ) it is well-known that the zero-frequency shot-noise spectral power is given by 3,4,5where T p are n = min(N 1 , N 2 ) transmission eigenvalues of a conductor, G 0 is the conductance quantum, and N 1,2 denotes the number of scattering channels in each of the two leads. T p are mutually correlated random numbers between 0 and 1 whose distribution depends on the type of the conductor. In the case of chaotic cavities considered below, universal fluctuations of T p are believed to be provided by the random matrix theory (RMT).6,7 The latter is characterized by the symmetry index β, distinguishing between universality classes of systems according to the absence (β = 2, unitary ensemble) or presence (β = 1, orthogonal ensemble) of timereversal symmetry and spin-flip symmetry (β = 4, symplectic ensemble). Various RMT related aspects of the shot noise are under active study now, both theoretically 8,9,10,11,12,13,14 and experimentally 15,16 (see also the references in these papers). However, exact results for the average shot-noise power P were reported in the literature only in the limiting cases of N 1,2 ≫ 1 2,17 (which is the purely classical one) 8,18 or19 the experimentally relevant case of few channels being an open problem.An alternative consideration was undertaken very recently by Braun et al.,20 who developed the semiclassical trajectory approach to build up the 1/N expansion for P , extending earlier results 21,22 to all orders of the inverse total number of channels, N = N 1 + N 2 (see also Ref. 23). They were able (for β = 1, 2) to sum up the resulting series in a compact form, which we represent introducing β as follows:. (2) This result surprisingly turned out to remain valid down to N 1,2 = 1, as was checked by comparison to numerics.Our aim here is to provide the exact RMT derivation of Eq. (2) valid at arbitrary N 1,2 and all β. There are several ways to perform the calculation. First, T p are defined as the singular values of a transmission matrix t (which is a N 1 ×N 2 off-diagonal block of a N ×N unitary scattering matrix).5 Finding P = P 0 tr [tt † (1 − tt † )] amounts thus to an integration over the unitary group which is a quite complicated problem in general. 24 Second, one can think of (1) a...

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Shot noise in chaotic cavities with an arbitrary number of open channels

Savin

Sommers

2006

Phys. Rev. B

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“…They determine, therefore, the optical S matrix. The long-lived states however feature indeterministic processes corresponding to the universal prediction of random matrix theory [4]. They cause the fluctuations of the transmission probability.…”

Section: A Eigenvalues and Transmissionmentioning

confidence: 99%

“…Short-lived whispering gallery modes are formed by attaching the leads in a suitable manner to cavities of different shape with convex boundary [3]. These direct processes can result in deterministic transport as signified by a striking system-specific suppression of shot noise [4]. The corresponding pathways are localized inside the cavities: the whispering gallery modes near to the convex boundary and the bouncing ball modes around the shortest pathway between the two attached leads [3].…”

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confidence: 99%

Spectroscopic properties of large open quantum-chaotic cavities with and without separated time scales

Bulgakov

Rotter

2006

Phys. Rev. E

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The spectroscopic properties of an open large Bunimovich cavity are studied numerically in the framework of the effective Hamiltonian formalism. The cavity is opened by attaching two leads to it in four different ways. In some cases, the transmission takes place via standing waves with an intensity that closely follows the profile of the resonances. In other cases, short-lived and long-lived resonance states coexist. The short-lived states cause traveling waves in the transmission while the long-lived ones generate superposed fluctuations. The traveling waves oscillate as a function of energy. They are not localized in the interior of the large chaotic cavity. In all considered cases, the phase rigidity fluctuates with energy. It is mostly near to its maximum value and agrees well with the theoretical value for the two-channel case.

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“…Both time scales are well separated from one another. A theoretical example are the shortlived whispering gallery modes in a small microwave cavity with convex boundary which coexist with many long-lived states, for details see [20][21][22]. An experimental example are the isobaric analogue resonances in medium -mass nuclei.…”

Section: Resonance Trapping and Dynamical Phase Transitionsmentioning

confidence: 99%

Dynamical Phase Transitions in Quantum Systems

Rotter¹

2010

JMP

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Many years ago Bohr characterized the fundamental differences between the two extreme cases of quantum mechanical many-body problems known at that time: between the compound states in nuclei at extremely high level density and the shell-model states in atoms at low level density. It is shown in the present paper that the compound nucleus states at high level density are the result of a dynamical phase transition due to which they have lost any spectroscopic relation to the individual states of the nucleus. The last ones are shell-model states which are of the same type as the shell-model states in atoms. Mathematically, dynamical phase transitions are caused by singular (exceptional) points at which the trajectories of the eigenvalues of the non-Hermitian Hamilton operator cross. In the neighborhood of these singular points, the phases of the eigenfunctions are not rigid. It is possible therefore that some eigenfunctions of the system align to the scattering wavefunctions of the environment by decoupling (trapping) the remaining ones from the environment. In the Schrödinger equation, nonlinear terms appear in the neighborhood of the singular points.

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Shot noise and transport in small quantum cavities with large openings

Cited by 31 publications

References 36 publications

Shot noise in chaotic cavities with an arbitrary number of open channels

Shot noise in chaotic cavities with an arbitrary number of open channels

Spectroscopic properties of large open quantum-chaotic cavities with and without separated time scales

Dynamical Phase Transitions in Quantum Systems

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